Gradient Method

Gradient methods are iterative optimization algorithms that aim to find the minimum (or maximum) of a function by repeatedly stepping in the direction of the negative (or positive) gradient. Current research focuses on improving the efficiency and robustness of these methods, particularly for non-convex problems arising in deep learning and other applications, exploring variations like stochastic gradient descent, adaptive methods (e.g., Adam), and incorporating second-order information or preconditioning techniques. These advancements are crucial for training complex models, enabling progress in fields like scientific machine learning and improving the performance of various machine learning tasks.